1/2y=y-7

Solution for 1/2y=y-7 equation:

1/2y=y-7

We move all terms to the left:

1/2y-(y-7)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y+7=0

We multiply all the terms by the denominator


-y*2y+7*2y+1=0

Wy multiply elements

-2y^2+14y+1=0

a = -2; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·(-2)·1
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{51}}{2*-2}=\frac{-14-2\sqrt{51}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{51}}{2*-2}=\frac{-14+2\sqrt{51}}{-4}
$